What is the derivative of y=(x^2)/(e^{2x)} ?

The derivative of y=(x^2)/(e^{2x)} is (2x(1-x))/(e^{2x)}

What is the first derivative of y=(x^2)/(e^{2x)} ?

The first derivative of y=(x^2)/(e^{2x)} is (2x(1-x))/(e^{2x)}

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derivative of

y = \frac{x ^{2}}{e ^{2 x}}

\frac{2 x ( 1 - x )}{e ^{2 x}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{e ^{2 x}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x ^{2} ) e ^{2 x} - \frac{d}{d x} ( e ^{2 x} ) x ^{2}}{( e ^{2 x} ) ^{2}}

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (e^{2 x}) = e^{2 x} \cdot 2

= \frac{2 x e ^{2 x} - e ^{2 x} \cdot 2 x ^{2}}{( e ^{2 x} ) ^{2}}

Simplify

\frac{2 x e ^{2 x} - e ^{2 x} \cdot 2 x ^{2}}{( e ^{2 x} ) ^{2}} : \frac{2 x ( 1 - x )}{e ^{2 x}}

= \frac{2 x ( 1 - x )}{e ^{2 x}}

\frac{\partial}{\partial x} (5 x^{2} + x y + 2 y^{2})

x \to 4 - lim (\frac{4}{x - 4})

\frac{d}{d y} (\frac{y ^{3}}{39} + \frac{13}{4 y})

5 x^{4}

\frac{d}{d x} (x^{3} + 3 x y^{2} - 15 x - 12 y)

What is the derivative of y=(x^2)/(e^{2x)} ?
The derivative of y=(x^2)/(e^{2x)} is (2x(1-x))/(e^{2x)}
What is the first derivative of y=(x^2)/(e^{2x)} ?
The first derivative of y=(x^2)/(e^{2x)} is (2x(1-x))/(e^{2x)}